Suppose M is a 3 \times 2 matrix.
How many rows does M have?
How many columns does M have?
State how many elements are there in the following:
A matrix with 4 rows and 5 columns.
The third column of a 7 \times 8 matrix.
The leading diagonal of a 4 \times 4 matrix.
A square matrix with 5 rows.
State the dimensions of the following matrices in the form m \times n:
State the entry at a_{23} \text{ in } A = \begin{bmatrix} -2 & -5 & 5 \\ -1 & 1 & -7 \\ 8 & 4 & 7\end{bmatrix}.
State the location of 5 in the form a_{ij} for the matrix A=\begin{bmatrix} -3 & 5 & -4 \\ 3 & -5 & 1 \\ -6 & -1 & 6 \end{bmatrix}.
Consider A=\begin{bmatrix} -5 & -8 & -9 \\ -6 & 2 & 8 \end{bmatrix} and B= \begin{bmatrix} 7 & -9 \\ 3 & 6 \\ -2 & 4 \end{bmatrix}. Find:
a_{21} - b_{11}
a_{13} \times b_{31}
M is a 3 \times 3 matrix. The elements of M are determined by the rule m_{ij}=i + 2 j + 1. Write down the matrix M.
A is a 3 \times 2 matrix. The elements of A are determined by the rule a_{ij} = i + 2 j - 2. Write down the matrix A.
B is a 4 \times 4 matrix. The elements of B are determined by the rule b_{ij} = i^2 . Write down the matrix B.
C is a 3 \times 3 matrix. The elements of C are determined by the rule c_{ij} = 2i + 2 j. Write down the matrix C.
A matrix with three less rows than columns has 54 elements. Find the dimensions of this matrix.
If a matrix has 10 elements, list the different dimensions it could possibly have.
Explain the dimension requirements of two matrices A and B to be able to:
Add or subtract them.
Perform the matrix multiplication A times B.
Define:
A matrix
A square matrix
A row matrix
An identity matrix
If a column matrix contains 6 elements, state the number of rows the matrix has.
State the number of columns the identity matrix I_4 contains.
Which of the following matrices is a square matrix?
Which of the following matrices is a zero matrix?
Write down an example of the following:
A row matrix consisting of the numbers -4, 1 \text{ and } 4.
A column matrix consisting of the numbers 5, -2, 2 \text{ and } 4.
A 2 \times 2 identity matrix.
A 3 \times 3 zero matrix.
A 3 \times 3 lower triangular matrix.
A 3 \times 3 upper triangular matrix.
A 3 \times 3 diagonal matrix with the numbers 5, 6 \text{ and } 1 on the leading diagonal.
Find the value of x \text{ and } y in the following equations:
Consider the equation \begin{bmatrix} t+4 & 5 & 7 \\ 9 & 6-v & w-6 \\ 6 & 8 & 5y \end{bmatrix}=\begin{bmatrix} 3 & 5 & u \\ x+7 & v & 2 \\ 6 & 8 & y \end{bmatrix}.
Determine the value of:
t
u
v
w
x
y
Find the value of w,x,y and z in the following equations:
The table shows the number of customers walking through the doors of two businesses over the long weekend:
Construct a matrix based on the table.
State the dimensions of the matrix.
| Saturday | Sunday | Monday | |
|---|---|---|---|
| Cafe | 150 | 130 | 124 |
| Bakery | 134 | 133 | 115 |
The table shows the average temperature (in degrees Celsius) in two cities over the four seasons:
| Summer | Autumn | Winter | Spring | |
|---|---|---|---|---|
| Brisbane | 31 | 22 | 17 | 25 |
| Tripoli | 34 | 24 | 19 | 26 |
State the meaning of the numbers in the rows and columns if the data is organised into the matrix \begin{bmatrix} 31 & 34 \\ 22 & 24 \\ 17 & 19 \\ 25 & 26 \end{bmatrix}.
State the dimensions of the matrix.
The following are the costs of a train ticket during different periods:
-
Weekday: \$7 peak, \$4 off-peak
-
Weekend: \$12 peak, \$6 off-peak
-
Public Holiday: \$18 peak, \$10 off-peak
Construct a 3 \times 2 matrix, D, based on the following:
Let the rows represent the type of day, in the order Weekday, Weekend and Public Holiday and let the columns represent the time of day, in the order peak and off-peak from left to right.
Construct a 2 \times 3 matrix, T, based on the following:
Let the rows represent the time of day, in the order peak and off-peak from top to bottom and let the columns represent the type of day, in the order Weekday, Weekend and Public Holiday.
Jack, a chef, is known for the following two recipes:
Crazy Cookie which contains:
360 \text{ g} of yeast
410 \text{ g} of salt
340 \text{ g} of flour
230 \text{ g} of sugar
120 \text{ g} of honey
Scrumptious Surprise which contains:
420 \text{ g} of yeast
390 \text{ g} of salt
330 \text{ g} of flour
200 \text{ g} of sugar
80 \text{ g} of honey
Organise the amounts into a 2 \times 5 matrix.
It was down to four competitors in the final of a long jump competition:
Uther jumped 7.4\text{ m}, 5.7 \text{ m} and 7.5 \text{ m}.
Yuri jumped 6.7 \text{ m}, 7.3 \text{ m} and 6.9 \text{ m}.
Vincent jumped 7.1 \text{ m}, 5.9 \text{ m} and 6.8 \text{ m}.
Luigi jumped 5.6 \text{ m}, 6.1 \text{ m} and 6.3 \text{ m}.
Organise the data into a 3 \times 4 matrix.